The compact exceptional Lie algebra 𝔤𝔠₂ as a twisted ring group

This is the authors' abstract. We don't add key points for this paper.

A new highly symmetrical model of the compact Lie algebra g 2 c g^c_2 is provided as a twisted ring group for the group Z 2 3 Z_2^3 and the ring R ⊕ R R⊕ R . The model is self-contained and can be used without previous knowledge on roots, derivations on octonions or cross products. In particular, it provides an orthogonal basis with integer structure constants, consisting entirely of semisimple elements, which is a generalization of the Pauli matrices in s u ( 2 ) su(2) and of the Gell-Mann matrices in s u ( 3 ) su(3) . As a bonus, the split Lie algebra g 2 g_2 is also seen as a twisted ring group.